# What is the least common multiple of 7 and 3?

#### Understand the Problem

The question is asking for the least common multiple (LCM) of the numbers 7 and 3. To solve this, we will identify the smallest number that is a multiple of both 7 and 3.

21

The least common multiple of 7 and 3 is 21.

#### Steps to Solve

1. **Identify the multiples of each number**

List the first few multiples of 7 and 3.

Multiples of 7: 7, 14, 21, 28, 35, 42, ...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, ...

2. **Find the smallest common multiple**

Identify the smallest number that appears in both lists of multiples.
21 is the smallest multiple that appears in both lists.

3. **Use the prime factorization method (optional)**

Another method to find the LCM is by using the prime factorization of each number.
7 is a prime number, so the prime factorization of 7 is 7^1.
3 is also a prime number, so the prime factorization of 3 is 3^1.

LCM is found by taking the highest power of each prime number in the factorization.
So, LCM(7, 3) = 7^1 * 3^1 = 21.


The least common multiple of 7 and 3 is 21.